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I need to construct an interpolating function from a 2D array of data. The reason I need something that returns an actual function is, that I need to be able to evaluate the function as part of an expression that I need to numerically integrate.

For that reason, "interp2" doesn't cut it: it does not return a function.

I could use "TriScatteredInterp", but that's heavy-weight: my grid is equally spaced (and big); so I don't need the delaunay triangularisation.

Are there any alternatives?

Paul Floyd
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reddish
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3 Answers3

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(Apologies for the 'late' answer, but I have some suggestions that might help others if the existing answer doesn't help them)

It's not clear from your question how accurate the resulting function needs to be (or how big, 'big' is), but one approach that you could adopt is to regress the data points that you have using a least-squares or Kalman filter-based method. You'd need to do this with a number of candidate function forms and then choose the one that is 'best', for example by using an measure such as MAE or MSE.

Of course this requires some idea of what the form underlying function could be, but your question isn't clear as to whether you have this kind of information.

Another approach that could work (and requires no knowledge of what the underlying function might be) is the use of the fuzzy transform (F-transform) to generate line segments that provide local approximations to the surface.

The method for this would be:

  1. Define a 2D universe that includes the x and y domains of your input data
  2. Create a 2D fuzzy partition of this universe - chosing partition sizes that give the accuracy you require
  3. Apply the discrete F-transform using your input data to generate fuzzy data points in a 3D fuzzy space
  4. Pass the inverse F-transform as a function handle (along with the fuzzy data points) to your integration function

If you're not familiar with the F-transform then I posted a blog a while ago about how the F-transform can be used as a universal approximator in a 1D case: http://iainism-blogism.blogspot.co.uk/2012/01/fuzzy-wuzzy-was.html

To see the mathematics behind the method and extend it to a multidimensional case then the University of Ostravia has published a PhD thesis that explains its application to various engineering problems and also provides an example of how it is constructed for the case of a 2D universe: http://irafm.osu.cz/f/PhD_theses/Stepnicka.pdf

IainCunningham
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If you want a function handle, why not define f=@(xi,yi)interp2(X,Y,Z,xi,yi) ? It might be a little slow, but I think it should work.

Itai Rusinek
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If I understand you correctly, you want to perform a surface/line integral of 2-D data. There are ways to do it but maybe not the way you want it. I had the exact same problem and it's annoying! The only way I solved it was using the Surface Fitting Tool (sftool) to create a surface then integrating it.

After you create your fit using the tool (it has a GUI as well), it will generate an sftool object which you can then integrate in (2-D) using quad2d

I also tried your method of using interp2 and got the results (which were similar to the sfobject) but I had no idea how to do a numerical integration (line/surface) with the data. Creating thesfobject and then integrating it was much faster.

It was the first time I do something like this so I confirmed it using a numerically evaluated line integral. According to Stoke's theorem, the surface integral and the line integral should be the same and it did turn out to be the same.

I asked this question in the mathematics stackexchange, wanted to do a line integral of 2-d data, ended up doing a surface integral and then confirming the answer using a line integral!

Community
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abdulhaq-e
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  • While I appreciate your suggestion, I feel that you mis-understand my problem. – reddish Jul 03 '12 at 10:24
  • In Mathematica, what I want to do is readily accomplished using the "Interpolation" function (http://reference.wolfram.com/mathematica/ref/Interpolation.html). I am currently working for a customer that insists on Matlab, so I was wondering if that is possible. – reddish Jul 03 '12 at 10:33
  • Essentially, I need to turn a 2D table into an object "f" for which class(f) returns 'function_handle'. Evaluating f(x,y) should perform the interpolation at (x,y) with a reasonable degree of efficiency. – reddish Jul 03 '12 at 10:35
  • Maybe I misunderstood your question! As far as I know, you can't do this in MATLAB, at least not with the functions/toolboxes included in the program. However, I would like to know what type of integral you want to evaluate? I think you should edit the question and include the integral etc.. – abdulhaq-e Jul 03 '12 at 18:05
  • this question is not about the integral. – reddish Jul 07 '12 at 17:13